GATE CS 2011 Q64 — General Aptitude

Let us define the variables involved in the problem:

• Let $B$ be the initial backlog of orders.
• Let $R$ be the number of new orders received per day.
• Let $C$ be the shipping capacity of a single truck per day.

We can set up equations based on the two given scenarios:

Scenario 1: 7 trucks clear all orders at the end of the $4^{\text{th}}$ day.

Scenario 2: 3 trucks clear all orders at the end of the $10^{\text{th}}$ day.

Subtracting Equation 1 from Equation 2:

Substituting $C = 3R$ into Equation 1:

Now, let $N$ be the minimum number of trucks required to clear all pending orders by the end of the $5^{\text{th}}$ day. The total capacity of $N$ trucks over $5$ days must be at least the total orders accumulated by then:

Substitute $C = 3R$ and $B = 80R$ into the inequality:

Since $R > 0$, we divide both sides by $R$:

Since the number of trucks $N$ must be an integer, the minimum number of trucks required is $6$.